Unitary Fermi gas in the epsilon expansion

Abstract

We construct systematic expansions around four and two spatial dimensions for a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi gas can be understood as a weakly-interacting system of fermionic and bosonic degrees of freedom. To the leading and next-to-leading orders in the expansion over \epsilon=4-d, with d being the dimensionality of space, we determine the thermodynamic functions, the fermion quasiparticle spectrum, the critical polarizations, and the critical temperature as functions of the binding energy of the two-body state. We also show that the unitary Fermi gas near two spatial dimensions reduces to a weakly-interacting Fermi gas and calculate the thermodynamic functions and the fermion quasiparticle spectrum in the expansion over \bar\epsilon=d-2. We discuss the matching of the two systematic expansions around four and two spatial dimensions in order to extract physical observables at d=3. We find good agreement of the results with those from recent Monte Carlo simulations.